Gaussian Atemporality: When Gaussian Quantum Correlations Imply Common Cause

TL;DR

This paper introduces the concept of Gaussian atemporality in quantum correlations, demonstrating that certain Gaussian quantum correlations are inherently atemporal and cannot be explained by common causes, with implications for understanding quantum causality.

Contribution

The paper defines Gaussian atemporality, introduces a robustness measure for it, and shows its operational significance and relation to quantum correlations beyond entanglement.

Findings

Gaussian atemporality robustness can be efficiently computed.

It reveals an intrinsic arrow of time in specific spatiotemporal correlations.

It measures quantum correlations beyond entanglement.

Abstract

Conventionally, covariances do not distinguish between spatial and temporal correlations. The same covariance matrix could equally describe temporal correlations between observations of the same system at two different times or correlations made on two spatially separated systems that arose from some common cause. Here, we demonstrate Gaussian quantum correlations that are `atemporal', such that the covariances governing their quadrature measurements are unphysical without postulating some common cause. We introduce Gaussian atemporality robustness as a measure of atemporality, illustrating its efficient computability and operational meaning as the maximum noise which can be added without removing this uniquely quantum phenomenon. We illustrate that (i) specific spatiotemporal Gaussian correlations possess an intrinsic arrow of time, such that Gaussian atemporality robustness is zero in one temporal direction and not the other and (ii) that it measures quantum correlations beyond entanglement.